A certain imprecision exists in an operation performed in a computer due to the characteristics of the hardware used to represent real numbers in the computer. Due to the finite size of memory storage in a computer, non-terminating real numbers are represented with a certain number of significant digits after either truncation or rounding. These numbers are referred to as floating-point numbers. Once the real numbers are represented as floating-point numbers, further imprecision arises because arithmetic operations performed by a computer generally involve further truncation or rounding.
For periodic functions such as trigonometric functions, the large input argument can be reduced in magnitude to a smaller reduced argument that allows more manageable evaluations of the function. The smaller reduced arguments are obtained from identities for periodic functions. For example, the sine and cosine functions satisfy the following relations:sin(x)=sin(x+2πN), and  Equation (1)cos(x)=cos(x+2πN),  Equation (2)where N is an integer.
In evaluation of the trigonometric functions on a computer having a specific machine precision, the performance of argument reductions may be problematic when the argument x is large since the period 2π is an irrational real number. Since the period is irrational, the argument reduction is, in itself, approximate when performed in a computer. In a computer, only an approximation to π may be represented. As the magnitude of the input argument increases, more and more digits of π, (more commonly π/2 or 2/π if the argument x is reduced to a range
            [                        -                      π            4                          ,                  π          4                    ]        )    ,will be involved in the argument reduction, and it may not result in an accurate outcome.